If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is
$\frac{1}{8}$
$\frac{2}{{21}}$
$\frac{1}{{32}}$
$\frac{1}{{35}}$
Ten students are seated at random in a row. The probability that two particular students are not seated side by side is
Out of $40$ consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is
If out of $20$ consecutive whole numbers two are chosen at random, then the probability that their sum is odd, is
A lot consists of $12$ good pencils, $6$ with minor defects and $2$ with major defects. A pencil is choosen at random. The probability that this pencil is not defective is
Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are picked at random, the probability that $A$ and $B$ have the same number of elements, is